# Circular motion with friction and banking - resultant forces

1. Jun 22, 2007

### exi

1. The problem statement, all variables and given/known data

A car travels 76 m/s around a circular track with a 111 m radius.

The car's mass is 2500 kg, the track is angled at 21°, and the coefficient of friction is 0.18.

What is the magnitude of the resultant force on the car and driver, expressed as kN?

3. The attempt at a solution

Double-checking my work here to see if I'm understanding this correctly.

If:
Fk = µ*Fn
Fn = mg/cosΘ
Fc = mv²/r

Then:
Fc = 130090.09 N
Fk = 4723.75 N

Which leaves me with two questions: Is the above correct, and what am I leaving out of the forces before summing them?

editing this to add: I've gotten a series of formulas that produce the correct answer, but I do not know where they are derived from. If anyone could help explain this, I'd appreciate it.

1. $$A = \frac {m(v^2cos\theta - grsin\theta)}{r}$$

2. $$B = \frac {mg + Asin\theta}{cos\theta}$$

3. $$(\mbox{Answer expressed in kN}) = \frac {Acos\theta + Bsin\theta}{1000}$$

Last edited: Jun 22, 2007
2. Jun 23, 2007

### CaptainZappo

If an object is moving in uniform circular motion, the NET force on that object must be equal to (mv^2)/r. You have this value recorded as Fc. You should note that Fc is NOT a single force, but rather is the NET force on the object in question.

The three formulas you've listed end up spitting out the exact same value as Fc, although in a very convoluted way.

3. Jun 23, 2007

### exi

Oh wow, you're right - what I did in the first 30 seconds answered the problem, but I didn't know I actually had the answer. I had to call someone in class with me who was given that formula system by a physics tutor.

That's... definitely something. :shy:

4. Oct 26, 2011

### brianonyango2

hallo exi may you explain the set of fomulas listed below the senteces in red...@all...i have a problem in calculatiion of forces in a free body diagram...any body who can help?

5. Oct 26, 2011

### grzz

We have to start from a FBD.

Try to find the forces which act on the car.